Gene targeting by means of homologous recombination between exogenous DNA and endogenous homologous chromosomal sequences has proven to be a great tool to create a designed mutation or correct a gene mutation in cultured mammalian cells in mice, including mouse embryonic stem (ES cells) and upon "injection of the targeted E cells", to transmit these mutations into the mouse germline (Smithies et al., Nature, 317:230-234, 1985; Thomas et al., Cell, 51:503-512, 1987; Koller et al., Proc. Natl. Acad, Sci. USA, 86:8927-8931, 1989; Kuhn et al., Science, 254:707-710, 1991; Thomas et al., Nature, 346:847-850, 1990; Schwartzberg et al., Science, 246:799-803, 1989; Doetschman et al., Nature, 330:576-578, 1987; Thomson et al., Cell, 5:313-321, 1989; Shesely et al., Proc. Natl. Acad. Sci. USA, 88:4294-4298, 1991). It is also well appreciated in the field that the ability to create large deletions by gene targeting would be extremely useful, especially with respect to large genes or complexed loci which contain gene clusters and/or multiple copies. In these genes, complete targeting usually requires sequential targeting using differential markers which necessitates longer passages of the ES cells, during which transmission capability to germline may be reduced. Also for primary mammalian cells longer passages may affect their propensity to differentiate. While good sized deletions of 15 kb have been achieved in the T-cell antigen receptor .beta.-subunit locus (Mombaerts et al., Proc. Natl. Acad. Sci. USA, 88:3084-3087, 1991), there remains a significant need for a method by which even larger genomic deletions can be achieved.